Agresti A - Introduction to Categorical Data Analysis (2ed 2007)

Agresti A - Introduction to Categorical Data Analysis (2ed 2007)

(Parte 1 de 9)

An Introduction to Categorical Data Analysis

Second Edition

Department of Statistics

University of Florida Gainesville, Florida

“ffirs” — 2007/1/31 — pagei—# 1 “ffirs” — 2007/1/31 — pagei—# 1

“ffirs” — 2007/1/31 — pagei—# 1

An Introduction to Categorical Data Analysis

An Introduction to Categorical Data Analysis

Second Edition

Department of Statistics

University of Florida Gainesville, Florida

Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data

Agresti, Alan

An introduction to categorical data analysis / Alan Agresti. p. cm.

Includes bibliographical references and index. ISBN 978-0-471-22618-5 1. Multivariate analysis. I. Title.

Printed in the United States of America. 10987654321

Contents

Preface to the Second Edition

1. Introduction

1.1 Categorical Response Data, 1

1.1.1 Response/Explanatory Variable Distinction, 2 1.1.2 Nominal/Ordinal Scale Distinction, 2 1.1.3 Organization of this Book, 3

1.2 Probability Distributions for Categorical Data, 3

1.2.1 Binomial Distribution, 4 1.2.2 Multinomial Distribution, 5

1.3 Statistical Inference for a Proportion, 6

1.3.1 Likelihood Function and Maximum Likelihood Estimation, 1.3.2 Significance Test About a Binomial Proportion, 8 1.3.3 Example: Survey Results on Legalizing Abortion, 8 1.3.4 Confidence Intervals for a Binomial Proportion, 9

1.4 More on Statistical Inference for Discrete Data, 1

1.4.1 Wald, Likelihood-Ratio, and Score Inference, 1 1.4.2 Wald, Score, and Likelihood-Ratio Inference for

Binomial Parameter, 12 1.4.3 Small-Sample Binomial Inference, 13 1.4.4 Small-Sample Discrete Inference is Conservative, 14 1.4.5 Inference Based on the Mid P-value, 15 1.4.6 Summary, 16

Problems, 16

2. Contingency Tables

2.1 Probability Structure for Contingency Tables, 21

2.1.1 Joint, Marginal, and Conditional Probabilities, 2 2.1.2 Example: Belief in Afterlife, 2

2.1.5 Binomial and Multinomial Sampling, 25 2.2 Comparing Proportions in Two-by-Two Tables, 25

2.2.1 Difference of Proportions, 26 2.2.2 Example: Aspirin and Heart Attacks, 26 2.2.3 Relative Risk, 27

2.3 The Odds Ratio, 28

2.3.1 Properties of the Odds Ratio, 29 2.3.2 Example: Odds Ratio for Aspirin Use and Heart Attacks, 2.3.3 Inference for Odds Ratios and Log Odds Ratios, 30 2.3.4 Relationship Between Odds Ratio and Relative Risk, 32 2.3.5 The Odds Ratio Applies in Case–Control Studies, 32 2.3.6 Types of Observational Studies, 34

2.4 Chi-Squared Tests of Independence, 34

2.4.1 Pearson Statistic and the Chi-Squared Distribution, 35 2.4.2 Likelihood-Ratio Statistic, 36 2.4.3 Tests of Independence, 36 2.4.4 Example: Gender Gap in Political Affiliation, 37 2.4.5 Residuals for Cells in a Contingency Table, 38 2.4.6 Partitioning Chi-Squared, 39 2.4.7 Comments About Chi-Squared Tests, 40

2.5 Testing Independence for Ordinal Data, 41

2.5.1 Linear Trend Alternative to Independence, 41 2.5.2 Example: Alcohol Use and Infant Malformation, 42 2.5.3 Extra Power with Ordinal Tests, 43 2.5.4 Choice of Scores, 43 2.5.5 Trend Tests for I × 2 and 2 × J Tables, 4 2.5.6 Nominal–Ordinal Tables, 45

2.6 Exact Inference for Small Samples, 45

2.6.1 Fisher’s Exact Test for 2 × 2 Tables, 45 2.6.2 Example: Fisher’s Tea Taster, 46 2.6.3 P-values and Conservatism for Actual P(Type I Error), 47 2.6.4 Small-Sample Confidence Interval for Odds Ratio, 48

2.7 Association in Three-Way Tables, 49

2.7.1 Partial Tables, 49 2.7.2 Conditional Versus Marginal Associations: Death

Penalty Example, 49 2.7.3 Simpson’s Paradox, 51 2.7.4 Conditional and Marginal Odds Ratios, 52 2.7.5 Conditional Independence Versus Marginal Independence, 2.7.6 Homogeneous Association, 54

(Parte 1 de 9)

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